1. Field of the Invention
The invention relates generally to the field of photolithography and more particularly to an improved method and system of optical proximity correction in photolithography design using a complementary mask and exchange design methodology.
2. Description of the Related Art
Microlithography is the technology of reproducing patterns using light. As presently used in semiconductor industry, a photomask pattern for a desired circuit is transferred to a wafer through light exposure, development, etch, and resist strip, etc. As feature sizes on a circuit become smaller and smaller, the circuit shape on the wafer differs from the original mask pattern more and more. In particular, corner rounding, line end foreshortening, iso-dense print bias, etc. are typically observed. These phenomena are called optical proximity effects.
One of main reasons for optical proximity effects is light diffraction. Optical proximity effects coming from light diffraction can be overcome partly if one has the choice of using a shorter wavelength source of light, with a projection system possessing a larger numerical aperture. In practice, the wavelength of an optical light source is typically fixed (365 nm for i line, 248 nm and 193 nm for DUV, etc.) and there is a practical upper limit on numerical aperture. So other resolution enhancement methods, including the use of phase-shifting masks and masks with serifs, have been developed to correct optical proximity effects.
Figure 1A shows an elbow shaped mask (the right-angled gray image), and corresponding aerial image after light exposure (or the final photoresist pattern after further development, etch, and resist strip, etc.) as the dashed lines. Similarly, FIG. 1E shows a 45-degree-turn mask (the 45 degree angled gray image), and corresponding aerial image after light exposure (or the final photoresist pattern after further development, etch, and resist strip, etc.) as the dashed lines. Comer rounding appears at both inner comer L and outer comer C as shown by the difference between the straight solid lines and the rounded dashed lines.
The following explanation presents a simple geometric picture for understanding the comer rounding shown in FIGS. 1A and 1E. For definiteness, it is assumed in the following discussion that the clear region of a mask is inside the mask and serif boundaries. Figures 1B-1D relate to aspects of FIG. 1A and FIGS. 1F-1H relate to aspects of FIG. 1E.
For incoherent light illumination (using either circular or rectangular aperture), the aerial image intensity at a point is given by the convolution between the intensity kernel function and the transmitted light intensity around the point, and is proportional to the volume of a truncated cone-type 3D structure. As shown in FIGS. 1B-1D and 1F-1H, the whole cone-type structure represents the intensity kernel function on a 2D region and is centered at that point and has a horizontal range r. The variable r is the resolution limit of the light source used in lithography. The truncation is done according to the actual light transmission around that point, which may be blocked by any opaque region in the photomask.
For an edge point E, that is shown separately in FIGS. 1B and 1F (when its distance to its nearest corner is larger than r), after truncation, its volume is half of whole volume under the intensity kernel function (i.e., half of whole volume of 3D cone-type structure).
For the outer corner C, that is shown separately in FIGS. 1C and 1G, after truncation, its volume is 1/4 and 3/8, respectively, of whole volume under the intensity kernel function (denoted "I" herein). Thus, I.sub.C =I.sub.E /2&lt;I.sub.E, for FIG. 1C and I.sub.C =3I.sub.E /4&lt;I.sub.E for FIG. 1G, independently of the range r and the form of the intensity kernel function.
The aerial intensity contour line passing through the edge point E will not pass through the outer comer C. Rather, it passes inside the elbow (see the dashed curve in FIGS. 1A and 1E). On the other hand, for the inner comer L, (that is shown separately in FIGS. 1D and 1H) after cut, its volume is 3/4 and 5/8, respectively, of whole volume under the intensity kernel function. Consequently, I.sub.L =3I.sub.E /2&gt;I.sub.E for FIG. 1D and I.sub.L =5I.sub.E /4&gt;I.sub.E for FIG. 1H, independently of the range r and the form of the intensity kernel function. The aerial intensity contour line passing through the edge point E will not pass through the inner corner L, but rather passes outside the elbow. This is referred to as corner rounding.
For coherent light illumination (with either circular or rectangular aperture), the aerial image intensity at a point is given by the square of the convolution between the amplitude kernel function and the actual transmitted light amplitude, and is proportional to the square of the volume of a truncated cone-type 3D structure. The whole cone-type structure represents the amplitude kernel function on a 2D region and is centered at that point and has a horizontal range r. The truncation is also done according to the actual light transmission around that point, which may be blocked by any opaque region in the photomask. For an edge point E (when its distance to its nearest corner is larger than r), after truncation, its volume is 1/2 of whole volume under the amplitude kernel function (i.e., half of whole volume of 3D cone-type structure). For the outer comer C, after cut, its volume is 1/4 (for FIG. 1C) or 3/8 (For FIG. 1G) of whole volume under the amplitude kernel function. Thus, I.sub.C =(1/2).sup.2 I.sub.E =I.sub.E /4&lt;I.sub.E in FIG. 1C and I.sub.C =(3/4).sup.2 I.sub.E =9I.sub.E /16&lt;I.sub.E in FIG. 1G, independently of the range r and the form of the amplitude kernel function. The aerial intensity contour curve passing through the edge point E will not pass through the outer comer C. Rather, it passes inside the elbow.
For the inner comer L, after truncation, its volume is 3/4 in FIG. 1D and 5/8 in FIG. 1H of whole volume under the amplitude kernel function. Thus, I.sub.L =(3/2).sup.2 I.sub.E =9I.sub.E /4&gt;I.sub.E for FIG. 1D and I.sub.C =(5/4).sup.2 I.sub.E =25I.sub.E /16&gt;I.sub.E for FIG. 1H, independently of the range r and the form of the amplitude kernel function. The aerial intensity contour curve passing through the edge point E will not pass through the inner comer L, but rather passes outside the elbow.
For partially coherent light illumination, the corner rounding can be understood qualitatively: The light contribution to the outer corner C comes from within a 1/4 circle region in FIG. 1C and 3/8 circle region in FIG. 1G of radius r (for circular aperture; for square aperture, it is from within a square region of length r), which is less than the contribution to an edge point E coming from within a half circle region of radius r. On the other hand, the light contribution to the inner corner L comes from within 3/4 circle region in FIG. ID and 5/8 circle region in FIG. 1H of radius r, which is more than the contribution to an edge point E coming from within a half circle region of radius r.